+
2%. T h e racy of t h e low temperature work w a s within reliability of t h e p r e s e n t work c a n only b e inferred, s i n c e d a t a for comparison a r e limited. T h e smooth c u r v e s which c a n b e drawn through t h e l o w and high temperature d a t a c a n b e t a k e n a s e v i d e n c e that t h e new thermostat introduced no u n s u s p e c t e d b i a s i n t h e high temperature data, A review of t h e b a s i c p r i n c i p l e s of t h e hot-wire t e c h n i q u e h a s revealed no r e a s o n for e x p e c t i n g p r o g r e s s i v e d e v i a t i o n s from t r u e v a l u e s a t higher temperat u r e s , e x c e p t p e r h a p s from convection. R e s u l t s p r e s e n t e d e a r l i e r (I) indicated no convection, e v e n with materials as fluid a s chloroform. A s t h e a p p a r a t u s u s e d i n t h e p r e s e n t work w a s t h e same, t h e factor which would h a v e t h e most significant contribution t o convection would b e v i s c o s i t y . At t h e highest temperatures u s e d , t h e v i s c o s i t y of t h e most fluid compound considered only approached that of chloroform. T h u s , t h e r e a p p e a r s t o b e no c a u s e for believing m a t convection w a s a f a c t o r i n t h e p r e s e n t measurements. Biphenyl and i t s chlorinated and alkylated d e r i v a t i v e s show very l i t t l e c h a n g e i n thermal conductivity with inc r e a s i n g temperature (see T a b l e I). P h o s p h a t e , carboxylate, and s i l i c a t e e s t t r s (see F i g u r e s 2 through 5 ) a l l show a s t e a d y d e c r e a s e i n thermal conductivity with i n c r e a s i n g temperature. A similar d e c r e a s e is observed with Dowtherm A (Dow Chemical Co.) ( F i g u r e 6), considering t h e experimental d a t a determined. i n t h i s work t o complement t h e work of Woolf and Sibbitt (3). A v a i l a b l e d a t a on d e n s i t y a n d v i s c o s i t y v a r i a t i o n s with
temperature f a i l e d t o s h o w correlations which would h a v e predicted t h i s difference i n behavior. S a k i a d i s and C o a t e s (2) predict t h a t p o s i t i v e , negative, and zero temperature c o e f f i c i e n t s of thermal conductivity a r e p o s s i b l e , b u t sufficient d a t a on t h e heat c a p a c i t y , velocity of sound, and intermolecular s p a c i n g i n t h e liquid s t a t e were not availa b l e for t h e p r e s e n t compounds t o permit u s e of their theoretical equation, T h e equation of S a k i a d i s and C o a t e s p r e d i c t s a l i n e a r variation of thermal conductivity with temperature. T h e curved l i n e s which were obtained over wide temperature r a n g e s , particularly with di-2-ethylhexyl s e b a c a t e , point up t h e need for modification of their treatment t o explain t h e s e r e s u l t s . T h e temperature coefficient d a t a for Aroclor 1 2 4 8 and Dowtherm A s h o u l d b e useful i n t h e d e s i g n of h e a t exc h a n g e r s utilizing t h e s e important heat transfer fluids.
CONCLUSIONS T h e s u c c e s s of t h i s present work h a s shown t h a t thermal conductivity v a l u e s c a n b e e a s i l y measured a t high temperatures. If s u i t a b l e l i q u i d s for t h e vapor bath a n d silversoldered or spot-welded l e a d s a r e u s e d , t h e method d i s c u s s e d should b e a p p l i c a b l e at higher temperatures.
LITERATURE CITED (1) C e c i l , 0. B . , Munch, R . H . , Znd. Eng. Chem. 48, 437 (1956). (2) Sakiadis, B. C., Coates, J., A.Z.Ch.E. Journal 1, 275 (1955). (3) Woolf, J. R . , Sibbitt, W. L.,Ind. Eng. Chem. 46, 1947 (1954). Received for review July 13, 1956.
Accepted November 3, 1956.
Heats of Solution of Polyindene JACK VANDERRYN AND A. C. ZETTLEMOYER Lehigh University, Bethlehem, Pa.
T h e physical-chemical behavior of high polymer-solvent s y s t e m s h a s received a great d e a l of attention i n recent years. On t h e other hand, t h e behavior of low molecular weight polymer s o l u t i o n s h a s not received much a t t e n t i o n i n s p i t e of t h e i r commercial importance. T h e p r e s e n t s t u d y w a s undertaken to i n v e s t i g a t e t h e nature of t h e interaction of a low molecular weight polyindene t y p e of polymer with solv e n t s or p l a s t i c i z e r s . Solubility measurements of t h i s polymer h a v e b e e n reported e l s e w h e r e (IO). P r e c i s e measurem e n t s of t h e h e a t of solution of polyindene a r e reported h e r e and form t h e b a s i s for a thermodynamic s t u d y of polyindene-solvent s y s t e m s . T h e u s u a l e x p r e s s i o n for t h e energy of mixing of none l e c t r o l y t e s i s given by t h e equation
AJP
=
V,B
V,(l-
V,)
(1)
where V , is t h e volume of solution i n c u b i c centimeters, V , i s t h e volume fraction of polymer, a n d B is g i v e n by t h e expression:
-
E = (SI S,)'
56
INDUSTRIA1 AND ENGINEERING CHEMISTRY
(2)
where SI and S, a r e t h e solubility parameters of s o l v e n t and polymer, respectively. T h e volume c h a n g e on mixing may be c o n s i d e r e d t o b e negligible a t low concentrations, s o t h a t t h e h e a t of mixing is equal t o t h e energy of mixing. According t o Equation 1 a plot of h E M / V m v s . V,(1 - V,) should g i v e a s t r a i g h t l i n e with s l o p e E . S i n c e B is a squared term, i t must b e p o s i t i v e and t h u s t h i s theory pred i c t s t h a t t h e h e a t of mixing of two nonelectrolytes must b e endothermic. However, where s p e c i f i c i n t e r a c t i o n s occur, t h e experimental v a l u e of B is not realized by Equation 2 but b e c o m e s more complex and often negative. Equation 1 may, however, s t i l l b e applicable.
E XP E RI M ENTAL Materials. Polymer. T h e polymer u s e d i n t h i s s t u d y w a s a coumarone i n d e n e resin manufactured b y t h e P e n n s y l v a n i a Industrial Chemical Corp. P r e v i o u s work i n t h i s laboratory on t h e molecular weight distribution, v i s c o s i t y , and solubility of t h i s r e s i n (5, 6, I O ) has b e e n reported. [ T h i s resin corresponds t o P i e s k i ' s (5) R e s i n I1 and t o Vanderryn's (IO) R e s i n IV.] T h e r e s i n w a s fractionated into four f r a c t i o n s VOL. 2 , NO. I
RESULTS
Table I. Polymer Properties Molecular weight
749 765 1023 105 'C. 86OC. 1.09 91.5% 7.9 7 ', 0.6%
Softening point Density Chemical a n a l y s i s
Fractions
(cryoscopic) (No. average) (wt. average) (ring and ball) (capillary) grams/cc. carbon hydrogen oxygen
Density, Grams/Cc.
Mol. Wt. (Cryoscopic)
Softening P t . , O c . (Capillary)
1.09 1.09 1.09 1. 15
1790 1350 842 401
162 135 94 27
x-1 x-2 x-3 x-5
U n f r a c t i o n a t e d P o l y m e r . T h e r e s u l t s of t h e h e a t of solution measurements for most of t h e s o l v e n t s (cyclohexane, 1-nitropane, nitrobenzene, e t h y l a c e t a t e , methyl ethyl k e t o n e , b e n z e n e , methylchloroform, carbon tetrachloride, bromobenzene, chlorobenzene, butyl chloride, sym-tetrachloroethane, and chloroform) a r e p r e s e n t e d in F i g u r e s 1 t o 3, where integral h e a t s of solution of polymer i n c a l . per 200 m l . of s o l v e n t a r e plotted v e r s u s volume fraction, V , , of polymer. V , h a s been used i n s t e a d of V,(1 - V , ) b e c a u s e in t h i s concentration range V , V , (1 - V,). T h e pertinent d a t a for a l l t h e s o l v e n t s which were u s e d a r e l i s t e d in T a b l e 11, which g i v e s a v e r a g e v a l u e s for t h e h e a t of s o l u t i o n per gram per 200 ml. of s o l v e n t , per ' b a s e mole (monomer unit) per 200 ml. solvent; C v a l u e s for Equation 1 t a k e n from t h e s l o p e s of t h e c u r v e s of F i g u r e s 1 t o 3; d i p o l e moments and solubility parameters for t h e s o l v e n t s ; and c a l c u l a t e d B v a l u e s assuming a s o l u b i l i t y parameter of 9.15 for t h e polymer. T h e v a l u e 9.15 w a s determined previously (10) and c o i n c i d e s with t h e parameter for b e n z e n e . T h i s r e s u l t is i n agreement with E q u a t i o n 1 s i n c e t h e h e a t of s o l u t i o n i n b e n z e n e i s approximately zero. T h e h e a t of solution per gram or per b a s e mole w a s cons t a n t (average deviation in 1w per gram w a s 5 % ) over t h e concentration range u s e d in t h i s s t u d y . On a mole fraction b a s i s t h e s o l u t i o n s w e r e extremely dilute-e.g., the highest concentration which w a s u s e d (methyl e t h y l ketone, run 24) corresponded t o a polymer mole fraction of 1.91 x Higher c o n c e n t r a t i o n s were not u s e d i n t h i s s t u d y b e c a u s e of (a)t h e difficulty of rapidly d i s s o l v i n g t h e polymer, ( b ) t h e high v i s c o s i t y of t h e r e s u l t i n g mixture, and (c) t h e p h y s i c a l limitations of t h e calorimeter. Intrinsic v i s c o s i t i e s for s o l u t i o n s of unfractionated polymer i n b e n z e n e , e t h y l a c e t a t e , 1-nitropropane, carbon tetrachloride, chlorobenzene, and sym-tetrachloroethane w e r e determined. T h e b e s t v a l u e s for t h e i n t r i n s i c v i s c o s i t y , 171, a r e l i s t e d i n T a b l e 111 a l o n g with t h e B v a l u e s obtained from t h e h e a t of s o l u t i o n measurements. F i g u r e 4 i l l u s t r a t e s t h e relation between B and [VI.
by P i e s k i and Zettlemoyer (5, 6) and t h e molecular weight fractions prepared by them were u s e d i n t h e p r e s e n t study. P e r t i n e n t properties of t h e polymer and i t s f r a c t i o n s a r e l i s t e d in T a b l e I . T h e c h e m i c a l a n a l y s i s s h o w s t h a t t h e r e s i n c o n t a i n s l i t t l e or n o coumarone s i n c e i t s oxygen cont e n t is q u i t e low. T h u s it will b e referred t o a s a polyi n d e n e polymer. -___ S o l v e n t s . T h e organic s o l v e n t s were reagent g r a d e chemic a l s , dried o v e r anhydrous magnesium s u l f a t e , and d i s t i l l e d . T h e b e n z e n e w a s w a s h e d with c o n c e n t r a t e d s u l f u r i c a c i d , dried over sodium, and d i s t i l l e d . Methods. I i e a t of Solution. T h e thermistor calorimeter which w a s u s e d t o m e a s u r e t h e h e a t s of solution h a s been d e s c r i b e d previously ( 9 , I I ) . Sample b u l b s w e r e blown from R m m . b o r o s i l i c a t e g l a s s tubing. F i n e l y powdered r e s i n w a s weighed into t h e bulbs, which were then s e a l e d off and p l a c e d in t h e s a m p l e holder of t h e calorimeter. T w o hundred milliliters of solvent w a s added t o t h e Dewar f l a s k , t h e s y s t e m w a s allowed t o equilibrate, and t h e s a m p l e bulb w a s broken under t h e liquid. T h e d e t a i l e d procedure used i s reported e l s e w h e r e (9). T h e c a l c u l a t e d calorimeter error, excluding t h e h e a t of breaking, w a s about f2%. Blank runs, made to determine t h e h e a t e f f e c t produced in breaking t h e s a m p l e bulb, g a v e a v e r a g e v a l u e s of - 0.02 c a l . for solv e n t s boiling above 1 0 0 ° C . and + 0.25 c a l . for more v o l a t i l e s o l v e n t s . In t h e l a t t e r c a s e t h e reproducibility w a s not very good, t h e a v e r a g e deviation being 0.04 cal. T h i s relatively l a r g e deviation i s in agreement with t h e findings of B a r t e l l and Suggitt ( I ) . T h e h e a t of s o l u t i o n measurements were made a t 2 6 ° C . T a b l e 11.
Solvent Cyclohexane 1-Nitropropane Nitrobenzene Ethyl a c e t a t e Anisole Methyl ethyl ketone n-Heptyl chloride Benzene Ethyl benzoate Ethylbenzene Methylchloroform Carbon tetrachloride Bromobenzene Chlorobenzene Butyl chloride Benzonitrile Pyridine Dimethylaniline s ym-Tetrachloroethane Chloroform a
Dipole Moment 0 3.3 4. 1 1.8 1.35 2.8 1.85 0 1.8 0.5 1.6 0
1.7 1.7 2.0 4. 1 2. 2 1.6 1.6 1.0
SIS
8.2 10.7 10.0 9.1 (8.5) 9.3
...
9.15 (7.8) 8.8 8.5 8.6 (8.9) 9.5 (8.4) 8.4 10.7 (8.4) (9.7) 9.3
F r a c t i o n a t e d P o l y m e r . T h e h e a t s of solution of f r a c t i o n s X-1, X-2, X-3, and X-5 in chloroform, chlorobenzene, a n d 1-nitropropane were measured and t h e v a l u e s i n c a l . per gram per 200 ml. a r e l i s t e d in T a b l e IV. T h e v a l u e for t h e unfractionated polymer i s l i s t e d for comparison.
H e o t s o f Solution o i Resin I V (Polyindene)
.!lH/Gram Ca1./200 M1. 3.52 2.01 1.09 1.00 0.49 0.46 0.36 0.01 0.16 0.33 0.42 0.59 0.92 0.93 0.96
- 1.04 - 1.61 - 1.95 - 4.48 - 4.80
I H / B a s e Mole Cal./200 MI. 40 7 232 127 116 57 53 42
-
1
- 19 - 39 - 48 - 68 - 107 - 108 - 112 - 121 - 187 - 226 - 519 - 558
B , Cal./Ml., Exptl. 3.96 2.22 1.25 1.14 0.5 0.5 0.4 0
- 0.2 - 0.37 - 0.44 - 0.63 - 1.01 - 1.01 - 1.06 - 1.1 - 1.42 - 2.1 - 2.9 - 5.2
B, CaL/Ml., Calcd 0.9 2.4 0.7 0 0.4
0.02
...
0 1.8 0.1 0.4 0.3 0.06 0.1 0.6 0.6 2.4 0.6
0.3 0.02
P a r a n t h e s e s indicate approximate values.
1957
CHEMICAL AND ENGINEERING DATA SERIES
57
T a b l e IV. Heats o f Solution o f Polyindene Fractions ( H e a t s i n col. per gram per 200 ml.)
I
Solvent
/JITROPROPANE
Fraction
Chloroform
Chlorobenzene
x-1 x-2 x-3 x-5
- 13.5 - 11.3 - 3.7 - 4.6 - 4.80
- 11.0 - 8.0 - 1.0 - 0.3 - 0.93
Unfractionated
I
r
f
tI -
A
.008
v?*
.012
001
Figure 1. Heat o f solution o f polyindene i n various solvents
DISCUSSION F i g u r e s 1, 2 , and 3 show t h a t within t h e l i m i t s of experimental error t h e integral h e a t of s o l u t i o n v a r i e s linearly with t h e volume fraction of polymer a s predicted by Equation l . T h e only exception t o t h i s i s carbon tetrachloride above 0.01 volume fraction of polymer. I n s p e c t i o n of T a b l e 11 s h o w s , however, t h a t t h e experimental v a l u e of B is not a t a l l in agreement with t h e theoretical v a l u e a s predicted from t h e solubility parameters by Equation 2. T h e experimental p o s i t i v e v a l u e s of B are, in general, larger than t h e predicted t h e o r e t i c a l values. T h e graph of B v a l u e s v e r s u s intrinsic v i s c o s i t y i n F i g u r e 4 i n d i c a t e s t h a t t h e polymer molecules tend t o uncurl i n t h e exothermic s o l v e n t s and remain i n a compact form in t h e endothermic s o l v e n t s . T h e s h a p e of t h e curve i s almost identical t o t h a t obtained by Daoust and Rinfret (2) for s o l u t i o n s of poly (vinyl acetate). T h e c u r v e s h o w s t h a t t h e maximum i n t r i n s i c v i s c o s i t y , and t h u s t h e apparent maximum length of t h e polymer c h a i n , i s attained a t r e l a t i v e l y low exothermic h e a t s of solution. A higher exothermic h e a t apparently d o e s not tend t o i n c r e a s e further t h e e f f e c t i v e length of t h e molecule in solution, and t h u s t h e i n c r e a s e d exothermicity of s o l v e n t s s u c h a s chloroform i s not d u e to p h y s i c a l e f f e c t s but must result from c h e m i c a l interactions. Similarly, a t low endothermic h e a t s t h e polymer molecule i s in a compact form preferring intrapolymer c o n t a c t s ; a g a i n larger endothermic h e a t s probably do not c a u s e further configurational c h a n g e s . T h e u s u a l explanation for exothermic h e a t s i s given a s t h e occurrence of s p e c i f i c interactions i n t h e mixture s u c h T a b l e 111.
Solvent sym-Tetrachloroethane Chlorobenzene Carbon tetrachloride Benzene Ethyl a c e t a t e I-Nitroprop ane
58
- 9.6 - 5.7 1.2 1.3 2.01
ACETATE
//ETHYL
c
.004
I-Nitropropane
a s s o l v a t i o n . For example, t h e exothermic h e a t s of solution of poly(viny1 a c e t a t e ) in chloroform have b e e n explained on the b a s i s of “ a c i d - b a s e ” interaction between t h e “ a c i d ” hydrogen of t h e chloroform and t h e “ b a s i c ” carbonyl oxygen of t h e polymer (2). No functional groups a s s u c h e x i s t in t h e polyindene molecule and t h u s s u c h a straightforward explanation c a n n o t b e offered. However, it i s instructive to compare t h e r e s u l t s of Hellfritz ( 4 ) on t h e h e a t of solution of p o l y s t y r e n e and t h o s e of D a o u s t and Rinfret (2) on poly(viny1 a c e t a t e ) with the r e s u l t s obtained in t h i s study. In F i g u r e 5 t h e r e s u l t s obtained by Hellfritz and by Daoust and Rinfret a r e plotted v e r s u s t h e r e s u l t s obtained in t h i s study for s o l v e n t s which were common t o both s t u d i e s . In both c a s e s t h e v a l u e s for toluene were compared tQ t h e v a l u e s for e t h y l b e n z e n e obtained in t h i s study. The u n i t s were used a s they were reported in t h e literature: .W per gram for polystyrene and B v a l u e s for poly(viny1 a c e t a t e ) . Inspection of F i g u r e 5 s h o w s t h a t there i s a regular relationship between t h e h e a t s of solution of polystyrene and polyindene e x c e p t for chlorcform. T h e h e a t of solution of polyindene in chloroform i s much more exothermic than would b e e x p e c t e d f r o m t h e polys t y r e n e d a t a . On t h e other hand, t h e chloroform and symtetrachloroethane d a t a for poly(viny1 a c e t a t e ) and polyindene seem t o follow a regular relationship. T h i s comparison sugg e s t s t h a t there may b e a similarity in t h e mechanism of t h e interaction of chloroform and sym-tetrachloroethane with low molecular weight polyindene and with poly(viny1 a c e t a t e ) .
0
D I Y E T H Y L ANILINE PYRIDINE @ BUTYL CHLORIDE
A
CHLOROBENZENE BROUOBEHZENE
0 CAR BOH TETRACHLORIDE
P
Intrinsic Viscosities
B , Cal./Ml.
- 4.9
[VI
- 1.01
0.053 0.056
-0.63 0.00 1.14 2.22
0.054
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.032 0.027 0.026
Figure 2. H e a t o f solution o f polyindene i n various solvents
VOL. 2, NO. I
- 12 0 TLTRACHLOROLTHANL 0 CnLORofOnY
i
-10
-8
t3
?
-I
4 V
-6
I
a -4
-2
C
5 a
XI0 Figure
3. H e a t
o f solution o f polyindene i n tetrachloroethane and in chloroform
T h i s mechanism apparently d o e s not o p e r a t e or i s not p r e s e n t t o a n y n o t i c e a b l e e x t e n t in t h e c a s e of p o l y s t y r e n e (molecular weight, 20,000). An i n s p e c t i o n of t h e v a l u e s for t h e h e a t s of solution of polyindene i n chloroform, sym-tetrachloroethane, methylchloroform, and carbon tetrachloride i n d i c a t e s t h a t t h e compounds c o n t a i n i n g “ a c i d ” hydrogens (chloroform and symtetrachloroethane) bring about high exothermic h e a t s w h i l e carbon t e t r a c h l o r i d e and methyl chloroform, which contain no “ a c i d ” hydrogen atoms, exhibit markedly lower exothermic h e a t s of solution. T h e “ b a s i c ” or e l e c t r o n donor groups, which must b e p r e s e n t for interaction with t h e a c i d hydrogen, may e x i s t in t h e form of terminal d o u b l e b o n d s in t h e polyi n d e n e m o l e c u l e (polyindene c o n t a i n s o n e terminal double bond per molecule). P o l y s t y r e n e of a high molecular weight h a s very few terminal double bonds and t h u s d o e s not exhibit t h i s interaction t o a n a p p r e c i a b l e e x t e n t . On t h e other hand, t h e low molecular weight polyindene h a s many more double b o n d s a v a i l a b l e for interaction. T h u s t h e high exothermic h e a t s of solution of polyindene i n chloroform a n d sym-tetrachloroethane a r e t e n t a t i v e l y attributed to “acidb a s e ” interaction. Further investigation of t h i s phenomenon u s i n g infrared absorption spectrophotometry i s i n progress. T h e experimental h e a t s of solution for most of t h e other s o l v e n t s may b e qualitatively explained on t h e b a s i s of s t r u c t u r e and t h e chemical nature of t h e s o l v e n t molecules. C y c l o h e x a n e e x h i b i t s a high endothermic h e a t of solution. T h i s molecule h a s n o polar groups a v a i l a b l e for solvents o l u t e i n t e r a c t i o n and i s not e a s i l y polarized. I t i s a poor s o l v e n t for t h e t y p e of polymer used in t h i s s t u d y and t h u s energy must b e supplied in order to bring a b o u t t h e solution process. On t h e other hand, b e n z e n e i s very s i m i l a r in s t r u c t u r e t o t h e polymer, h a s a highly p o l a r i z a b l e conjugated double bond s t r u c t u r e and yet no polar groups, and h a s a s o l u b i l i t y parameter e q u a l to that of t h e polymer. T h u s i t i s not s u r p r i s i n g t h a t t h e solution p r o c e s s i s athermal. T h e m o l e c u l e s which c o n t a i n oxygen a l l e x h i b i t endothermic or very low exothermic h e a t s . T h e s e compounds 1957
a r e not strongly “ a c i d i c ” or “ b a s i c , ” i n s o m e c a s e s may e x h i b i t s o m e a s s o c i a t i o n i n t h e pure liquid s t a t e , h a v e relatively high d i p o l e moments ( e s p e c i a l l y t h e nitro compounds and methyl e t h y l ketone), and h a v e l a r g e polar groups. S t e r i c e f f e c t s and t h e f a c t t h a t both t h e o x y g e n s and t h e polymer a r e e l e c t r o n d o n o r s would t h u s prevent polymer-solvent interaction. Within t h i s group of s o l v e n t s t h e i n f l u e n c e of t h e aromatic v e r s u s a l i p h a t i c s t r u c t u r e i s evident. In t h e p a i r s n i t r o b e n z e n e n i t r o p r o p a n e and e t h y l benzoate-ethyl a c e t a t e , t h e aromatic d e r i v a t i v e e x h i b i t s a lower endothermic h e a t b e c a u s e of s t r u c t u r a l similarity to t h e polymer. T h e importance of t h e length of t h e a l i p h a t i c c h a i n is evident by comparing t h e v a l u e for heptyl chloride, which e x h i b i t s a low endothermic h e a t , with butyl chloride, which i s exothermic. E f f e c t o f Molecular Weight. T h e i n c r e a s i n g exothermic h e a t s of s o l u t i o n with i n c r e a s i n g molecular w e i g h t may b e e x p l a i n e d by considering t h e s t a t e of t h e polymer a t room temperature. A polymer below i t s second-order t r a n s i t i o n temperature, T, , i s i n a thermodynamically u n s t a b l e s t a t e (7) and c a n b e c o n s i d e r e d a supercooled liquid. When t h e polymer is p l a c e d in solution, i n e f f e c t t h e t r a n s i t i o n temperature i s lowered, which l i b e r a t e s t h e e x c e s s f r e e energy of t h e u n s t a b l e s t a t e . In other words, t h e polymer i s i n a higher energy s t a t e i n t h e bulk “ s o l i d ” than i t is in solution. Ueberreiter and Kanig (8) h a v e shown t h a t t h e secondorder t r a n s i t i o n temperature of p o l y s t y r e n e v a r i e s linearly with t h e d e g r e e of polymerization, P, a c c o r d i n g t o t h e equation:
(3)
,
+3
+I
i I \ o f a
0
m -I
-3
-5
I
0.02
Figure 4.
I
I
0.04
H e a t o f solution
I 0.06
VS.
intrinsic viscosity
CHEMICAL AND ENGINEERING DATA SERIES
59
a
TETRACHLOROETHANE
0 BENZENE
CHLOROBENZENE
0
h
STYRENE
m’ E T H Y L
B
CHLOROFORM
A
where AC, is t h e difference in h e a t c a p a c i t y of t h e polymer above and below T,, and W , i s t h e c h e m i c a l interaction energy between polymer and solvent. T h e h e a t of solution of a polymer below t h e second-order t r a n s i t i o n point i s t h u s composed of a “ p h y s i c a l ” (first two terms o n right-hand s i d e of E q u a t i o n 4) and a chemical (W,) h e a t term. Above T, t h e h e a t of solution i s given by
M E T H Y L ETHYL KETONE
ACETATE
CYCLOHEXANE
T O L U E N E - E T H Y L BENZENE I
0
-4
-2
B o A L/YL.,
PO LYINDE PIE
-6
+2 I
Iw = w,
\a
\
\ UJ -6
14
\
POLYVIYYLAOCTATC
\’
2
\
w
a
\
>
IO
\
I-
F 8y 4 A
v)
3 -4
f>
0
a
6
\
-?.
\
-2
5
0
n
\
i
\
\ 0
2:
\.
m
\ v\ \
‘121 t2
-2
-4
CAL/Q.
2
+2
0 POLY I N D E N E
Figure 5. H e a t of solution of polyindene v s . polystyrene (4) and poly(viny1 a c e t d e )
(2)
where a and b a r e c o n s t a n t s . Von Gunner and S c h u l z (3) h a v e r e c e n t l y applied t h i s concept quantitatively and h a v e developed t h e following e q u a t i o n for t h e h e a t of solution of a polymer:
-
AC, AH = - (p) a (P + b / a )
I
(5)
A preliminary t e s t of t h i s theory by Von Gunner and Schulz
+ ThC, + w w
CHLOROFORM
(4)
P
4
-12 0
5
-8
(3) h a s shown t h a t E q u a t i o n s 4 and 5 a r e a p p l i c a b l e t o t h e h e a t s of s o l u t i o n of polystyrene i n various s o l v e n t s over a range of P v a l u e s from 30 t o 100, using v a l u e s for a, b, and AC, from t h e literature. T h e v a l u e s of their c o n s t a n t s a, b , and hC, a r e not a v a i l a b l e for polyindene. F i g u r e 6 s h o w s a P plot of AH vs. for polyindene (see T a b l e IV) a s P + b/a suming a v a l u e of 2.98 for b / a . T h e a c t u a l v a l u e of b / a d o e s not a f f e c t t h e s h a p e of t h e c u r v e s i n F i g u r e 6 but only s e r v e s t o s h i f t them along t h e a b s c i s s a . T h e s e r e s u l t s support t h e work of Von Gunner and Schulz. Inspection of F i g u r e 6 s h o w s t h a t t h e c u r v e s obtained for t h e three s o l v e n t s a r e parallel l i n e s drawn through t h e d a t a for t h e t h r e e h i g h e s t molecular weight f r a c t i o n s and l e v e l off sharply for t h e l o w e s t molecular weight fraction. S i n c e t h e l o w e s t molecular fraction (X-5)i s a v i s c o u s liquid, more d e n s e than t h e higher molecular weight fractions which a r e “ s o l i d s , ” i t s second-order transition temperature must b e below room temperature. Furthermore, t h e v a l u e s of T, a r e usually somewhat below t h e softening point of t h e polymer which i s 27°C. for fraction X-5 ( T a b l e I). E q u a t i o n 5 must t h u s b e u s e d for t h e h e a t of solution of fraction X - 5 , while E q u a t i o n 4 a p p l i e s t o t h e other fractions. T h u s , t h e h e a t of solution of fraction X-5 i s d u e only t o c h e m i c a l i n t e r a c t i o n s , w h e r e a s t h e h e a t s of solution of fractions X-1 and X-2 a r e a r e s u l t of both chemical and p h y s i c a l contributions. T h e higher exothermic h e a t of solution of fraction X-5 i n chloroform a s compared t o fraction X-3 i s explained by t h e fact t h a t X-5 h a s more double bonds a v a i l a b l e for interaction with t h e “ a c i d ” hydrogen of t h e chloroform. T h i s effect i s not evident i n s o l u t i o n s of chlorobenzene and nitropropane, b e c a u s e t h e s e s o l v e n t s do not h a v e a n y “ a c i d ” hydrogen atoms. I t h a s t h u s been shown that t h e theory of t h e “ s o l i d ” s t a t e of polymers e x p l a i n s t h e c h a n g e in h e a t of solution with molecular weight and i s a b l e t o differentiate between t h e “ p h y s i c a l ” and chemical contributions t o t h e h e a t of solution. ~
u
ACKNOWLEDGMENT
r a
T h i s work w a s supported by K e n t i l e , I n c . , Brooklyn, N . Y .
-4
LITERATURE CITED
0
+4
I-
W
1
0
0.5
0.6
4
0.7
8
0.8
REEIN I V
0.9
12 16 18
MOLECULAR WLIQHT X IO-‘ Figure 6. Heat o f solution v s . molecular weight
60
INDUSTRIAL AND ENGINEERING CHEMISTRY
U
(1) Bartell, F. E., Suggitt, R., J. P h y s . Chem. 58, 36 (1954). ( 2 ) Daoust, H., Rinfret, M., Can. J. Chem. 32, 492 (1954). (3) Gunner, K. von, Schulz, G., Naturwissenschaften 40, 164 (1953). (4) Hellfritz, H., Makromol. Chem. 7, 191 (1951). (5) P i e s k i , E., P h D . dissertation, Lehigh University, 1949. (6) P i e s k i , E., Zettlemoyer, A., Ind. Eng. Chem. 45, 167 (1953). (7) Small, P . , J. Appl. Chem. 3, 7 1 (1953). (8) Ueberreiter, K . , Kanig, G., Naturforscher 70, 630 (1952). (9) Young, G., Ph.D. dissertation, Lehigh University, 1954. (10) Zettlemoyer, A , Vanderryn, J . , I n d . Eng. Chern. 49, 220(1957). (11) Zettlemoyer, A., Young, G.,Chessick, J . , Healey, F . , J. P h y s . Chem. 57, 649 (1953).
R e c e i v e d for review J+y 5, 1956.
Accepted December 3, 1956.
Division of Paint, P l a s t i c s , and Printing Ink Chemistry, 129th Meeting, ACS, Dallas, T e x . , April 1956.
V O L . 2, NO. I
